Alexander Quaas Berger

Director del Programa Doctorado en Matemática

Línea de Investigación:

Análisis No-Lineal y de Ecuaciones Diferenciales Parciales

Información:

  • Grado Académico: Ph.D Universidad de Chile - Université de Paris-Dauphine (Francia)
  • Título Profesional: Ingeniero Civil Matemático, Universidad de Chile
  • Campus: Casa Central
  • Oficina: F-238
  • Email: alexander.quaas@usm.cl
  • Teléfono: (56) (32) 265 4489

Publicaciones Recientes

Núm. Autores Artículo Revista Año
75

G. Dávila, A. Quaas, E. Topp

Existence, nonexistence and multiplicity results for nonlocal Dirichlet problems

Journal of Differential Equations; Vol. 266(9), pp. 5971-5997; Apr. 2019.

2019
74

J. García-Melián, L. Iturriaga, A. Quaas

Liouville theorems for radial solutions of semilinear elliptic equations

Complex Variables and Elliptic Equations; Vol 64(6), pp. 933-949; 2019.

2019
73

G. Dávila, A. Quaas, E. Topp

An ODE approach for fractional Dirichlet problems with gradient nonlinearity

Mathematische Zeitschrift; Vol. 291(1–2), pp. 85–111; Feb. 2019.

2019
72

B. Barrios, J. García-Melián, A. Quaas

Periodic solutions for the one-dimensional fractional Laplacian

J. Differential Equations 267 (2019), no. 9, 5258–5289

2019
71

B. Barrios, J. García-Melián, A. Quaas

A note on the monotonicity of solutions for fractional equations in half-spaces

Proc. Amer. Math. Soc. 147 (2019), no. 7, 3011–3019

2019
70

M. Á. Burgos-Pérez, J. García-Melián, A. Quaas

Some nonexistence theorems for semilinear fourth-order equations

Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), no. 3, 761–779

2019
69

J. García-Melián, A. Quaas, B. Sirakov

Liouville theorems for nonlinear elliptic equations in half-spaces

Journal d’Analyse Mathématique; Vol. 139, pp. 559–583; Nov. 2019.

2019
68

A. Quaas, A. Rodríguez

Analysis of the attainment of boundary conditions for a nonlocal diffusive Hamilton-Jacobi equation

Discrete & Continuous Dynamical Systems – A, Vol. 38(10), pp 5221-5243, Oct. 2018.

2018
67

B. Barrios, L. Del Pezzo, J. García-Melián, A. Quaas

Symmetry results in the half-space for a semi-linear fractional Laplace equation

Annali di Matematica Pura ed Applicata, Vol. 197(5), pp 1385-1416, Oct. 2018.

2018
66

A. Quaas, E. Topp

Existence and uniqueness of large solutions for a class of non-uniformly elliptic semilinear equations

Journal d’Analyse Mathématique; Vol. 136(1), pp. 341–355; Oct. 2018.

2018
65

A. Quaas, A. Rodríguez

Loss of boundary conditions for fully nonlinear parabolic equations with superquadratic gradient terms

Journal of Differential Equations, Vol. 264(4), pp. 2897-2935, Feb. 2018.

2018
64

B. Barrios, L. Del Pezzo, J. García-Melián, A. Quaas

A priori bounds and existence of solutions for some nonlocal elliptic problems

Revista Matemática Iberoamericana, Vol. 34(1), pp. 195-220, Feb. 2018.

2018
63

C. Huyuan, A. Quaas

Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results

Journal of the London Mathematical Society, Vol. 97(2), pp. 196-221, Apr. 2018.

2018
62

A. Quaas, A. Xia

Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian

Communications in Contemporary Mathematics, Vol. 20(3), art. 1750032, May 2018.

2018
61

L.M. Del Pezzo, B. Barrios, J. García, A. Quaas

A Liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions

Discrete and Continuous Dynamical Systems – Series A; Vol. 37(11), pp. 5731-5746; Nov. 2017

2017
60

L.M. Del Pezzo, A. Quaas

A Hopf’s lemma and a strong minimum principle for the fractional p-Laplacian

Journal of Differential Equations; Vol. 263(1), pp. 765-778; Jul. 2017

2017
59

G. Dávila, A. Quaas, E. Topp

Continuous viscosity solutions for nonlocal Dirichlet problems with coercive gradient terms

Mathematische Annalen; Vol. 369(3-4), pp. 1211-1236; Dec. 2017

2017
58

A. Quaas, A. Xia

Existence and uniqueness of positive solutions for a class of logistic type elliptic equations in involving fractional Laplacian

Discrete and Continuous Dynamical Systems – Series A; Vol. 37(5), pp. 2653-2668; May 2017

2017
57

Gonzalo Dávila, Alexander Quaas, Erwin Topp

Continuous viscosity solutions for nonlocal Dirichlet problems with coercive gradient terms

Math. Ann. 369 (2017), no. 3-4, 1211–1236

2017
56

J. García, B. Barrios, L.M. Del Pezzo, A. Quaas

Monotonicity of solutions for some nonlocal elliptic problems in half-spaces

Calculus of Variations and Partial Differential Equations; Vol. 56, art. 39; Apr. 2017

2017
55

L.M. Del Pezzo, A. Quaas

Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian

Journal of Fixed Point Theory and Applications; Vol. 19(1), pp. 939-958; Mar. 2017

2017
54

A. Quaas O. González-Melendez

On critical exponents for Lane-Emden-Fowler-type equations with a singular extremal operator

Annali di Matematica Pura ed Applicata; Vol. 196(2), pp. 599-615; Apr. 2017

2017
53

L. del Pezzo, A. Quaas

Global Bifurcation for Fractional p-Laplacian and an Application

Zeitschrift für Analysis und Ihre Anwendungen; Vol. 35(4), pp. 411-447; 2016

2016
52

A. Quaas, A. Xia

Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions

Zeitschrift für angewandte Mathematik und Physik; Vol. 67(3), art. 40; Jun. 2016

Link

2016
51

J. García, S. Alarcón, M. Burgos, A. Quaas

Nonexistence results for elliptic equations woth gradient terms

Journal of Differential Equations; Vol. 260(1), pp. 758-780; Jan. 5, 2016.

2016
50

S. Alarcón, J. García, A. Quaas

Optimal Liouville theorems for supersolutions of elliptic equations with the Laplacian

Annali della Scuola Normale Superiore di Pisa-Classe di Scienze; Vol. XVI(1), pp. 129-158; 2016

2016
49

A. Quaas, A. Xia

A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian

Nonlinearity; Vol. 29(8), pp. 2279-2297; Aug. 2016

2016
48

M.A. Burgos, J. García, A. Quaas

Classification of Supersolutions and Liouville Theorems for some Nonlinear Elliptic Problems

Discrete and Continuous Dynamical Systems; Vol. 36(9), pp. 4703-4721; Sep. 2016

2016
47

B. Sirakov, J. García, A. Quaas

Elliptic equations with absorption in a half-space

Bulletin of the Brazilian Mathematical Society; Vol. 47(3), pp. 811-821; Sep. 2016

Link

2016
46

A. Quaas, H. Chen, P. Felmer

Large solutions to elliptic equations involving fractional Laplacian

Annales de L´Institut Henri Poincaré: Analyse Non Linéaire; Vol. 32(6), pp. 1199-1228; Nov-Dic. 2015

2015
45

H. Chen, P. Felmer, A. Quaas

Self-Generated Interior Blow-Up Solutions of Fractional Elliptic Equation with Absorption

Differential and Integral Equations; Vol. 28(9-10), pp. 839-860; Sept-Oct. 2015

Link

2015
44

A. Quaas, A. Xia

Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space

Calc. Var. Partial Differential Equations 52 (2015), no. 3-4, 641–659

2015
43

S. Alarcón, J. García-Mellán, A. Quaas

Existence and non-existence of solutions to elliptic equations with a general convection term

Proceedings of the Royal Society of Edinburgh, Section A-Mathematics; Vol. 144(2), pp. 225-239; Apr. 2014

2014
42

S. Alarcón, J. García-Melián, A. Quaas

Liouville Type Theorems for Elliptic Equations with Gradient Terms

 Milan Journal of Mathematics 81 (2013) 171-185

2013
41

S. Alarcón, J. García-Melián, A. Quaas

Nonexistence of positive supersolutions to some nonlinear elliptic problems

Journal de Mathématiques Pures et Appliquées Volume 99, Issue 5, May 2013, Pages 618-634

2013
40

S. Alarcón, A. Quaas

Large viscosity solutions for some fully nonlinear equations

NoDEA Nonlinear Differential Equations Appl. 20 (2013) 1453-1472

2013
39

P. Felmer, A. Quaas, B. Sirakov

Solvability of nonlinear elliptic equations with gradient terms

J. Differential Equations 254 (2013), no. 11, 4327–4346

2013
38

Salomón Alarcón, Jorge García-Melián, Alexander Quaas

Existence and uniqueness of solutions of nonlinear elliptic equations without growth conditions at infinity

Journal d’Analyse Mathématique October 2012, Volume 118, Issue 1, pp 83–104

2012
37

P. Felmer, A. Quaas, J. Tan

Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian

Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 6, 1237–1262

2012
36

Salomón Alarcón, Jorge García-Melián, Alexander Quaas 

Keller–Osserman type conditions for some elliptic problems with gradient terms

Journal of Differential Equations Volume 252, Issue 2, 15 January 2012, Pages 886-914

2012
35

P. Felmer, A. Quaas, B. Sirakov

Existence and regularity results for fully nonlinear equations with singularities

Math. Ann. 354 (2012), no. 1, 377–400

2012
34

S. Alarcón, L. Iturriaga, A. Quaas

Existence and multiplicity results for Pucci’s operators involving nonlinearities with zeros

Calculus of Variations and Partial Differential Equations November 2012, Volume 45, Issue 3–4, pp 443–454

2012
33

P. Felmer, A. Quaas

 

Fundamental solutions for a class of Isaacs integral operators

Discrete Contin. Dyn. Syst. 30 (2011), no. 2, 493–508

2011
32

R. Meneses, A. Quaas

Fujita type exponent for fully nonlinear parabolic equations and existence results

J. Math. Anal. Appl. 376 (2011), no. 2, 514–527

2011
31

P. Felmer, A. Quaas

Fundamental solutions and Liouville type theorems for nonlinear integral operators

Adv. Math. 226 (2011), no. 3, 2712–2738

2011
30

Alejandro Allendes, Alexander Quaas

Multiplicity results for extremal operators trough bifurcation

Discrete and Continuous Dynamical Systems – Series A, Vol. 29, No. 1, pp: 51–65, 2011

2011
29

S. Alarcón, A. Quaas

Large number of fast decay ground states to Matukuma-type equations

Journal of Differential Equations Volume 248, Issue 4, 15 February 2010, Pages 866-892

2010
28

Dávila, Gonzalo; Felmer, Patricio; Quaas, Alexander

Harnack inequality for singular fully nonlinear operators and some existence results

Calc. Var. Partial Differential Equations 39 (2010), no. 3-4, 557–578.

2010
27

M. J. Esteban, P. Felmer, A. Quaas

Eigenvalues for radially symmetric fully nonlinear operators

Comm. Partial Differential Equations 35 (2010), no. 9, 1716–1737

2010
26

P. Felmer, A. Quaas, B. Sirakov

Resonance phenomena for second-order stochastic control equations

SIAM J. Math. Anal. 42 (2010), no. 3, 997–1024

2010
25

P. Felmer, A. Quaas, B. Sirakov

Landesman-Lazer type results for second order Hamilton-Jacobi-Bellman equations

J. Funct. Anal. 258 (2010), no. 12, 4154–4182

2010
24

P. Felmer, A. Quaas, J. Tan

Geometry of phase plane and radial solutions for nonlinear elliptic equations with extremal operators.

J. Math. Anal. Appl. 366 (2010), no. 1, 101–111

2010
23

M. J. Esteban, P. Felmer, A. Quaas

Superlinear elliptic equation for fully nonlinear operators without growth restrictions for the data

Proc. Edinb. Math. Soc. (2) 53 (2010), no. 1, 125–141

2010
22

P. Felmer, A. Quaas, M. Tang, J. Yu

Random dynamics of gene transcription activation in single cells

J. Differential Equations 247 (2009), no. 6, 1796–1816

2009
21

P. Felmer, A. Quaas

Fundamental solutions and two properties of elliptic maximal and minimal operators

Trans. Amer. Math. Soc. 361 (2009), no. 11, 5721–5736.

2009
20

P. Felmer, A. Quaas, M. Tang

On the complex structure of positive solutions to Matukuma-type equations

Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, 869–887

2009
19

A. Quaas, B. Sirakov

Existence and non-existence results for fully nonlinear elliptic systems

Indiana Univ. Math. J. 58 (2009), no. 2, 751–788

2009
18

P. Felmer, M. Montenegro, A. Quaas

A note on the strong maximum principle and the compact support principle

J. Differential Equations 246 (2009), no. 1, 39–49

2009
17

Dávila, Gonzalo; Felmer, Patricio; Quaas, Alexander

Alexandroff-Bakelman-Pucci estimate for singular or degenerate fully nonlinear elliptic equations

C. R. Math. Acad. Sci. Paris 347 (2009), no. 19-20, 1165–1168

2009
16

P. Felmer, A. Quaas

Around viscosity solutions for a class of superlinear second order elliptic differential equations.

On the notions of solution to nonlinear elliptic problems: results and developments, 205–228, Quad. Mat., 23, Dept. Math., Seconda Univ. Napoli, Caserta, 2008

2008
15

A. Quaas, B. Sirakov

Solvability of monotone systems of fully nonlinear elliptic PDE’s

C. R. Math. Acad. Sci. Paris 346 (2008), no. 11-12, 641–644

2008
14

P. Felmer, A. Quaas, M. Tang, J. Yu

Monotonicity properties for ground states of the scalar field equation

Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 1, 105–119

2008
13

M.J. Esteban, P. Felmer, A. Quaas

Large critical exponents for some second order uniformly elliptic operators

Comm. Partial Differential Equations 32 (2007), no. 4-6, 543–556

2007
12

P. Felmer, A. Quaas

Critical exponents for uniformly elliptic extremal operators

Indiana Univ. Math. J. 55 (2006), no. 2, 593–629

2006
11

A. Quaas, B. Sirakov

On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators

C. R. Math. Acad. Sci. Paris 342 (2006), no. 2, 115–118

2006
10

P. Felmer, A. Quaas

Some recent results on equations involving the Pucci’s extremal operators

Contributions to nonlinear analysis, 263–281, Progr. Nonlinear Differential Equations Appl., 66, Birkhäuser, Basel, 2006

2006
9

A. Quaas, B. Sirakov

Existence results for nonproper elliptic equations involving the Pucci operator

Comm. Partial Differential Equations 31 (2006), no. 7-9, 987–1003

2006
8

P. Felmer, A. Quaas, M. Tang

On uniqueness for nonlinear elliptic equation involving the Pucci’s extremal operator

J. Differential Equations 226 (2006), no. 1, 80–98

2006
7

J. Busca, M. J. Esteban, A. Quaas

Nonlinear eigenvalues and bifurcation problems for Pucci’s operators

Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 2, 187–206

2005
6

A. Quaas

Existence of a positive solution to a “semilinear” equation involving Pucci’s operator in a convex domain

Differential Integral Equations 17 (2004), no. 5-6, 481–494

2004
5

P. Felmer, A. Quaas

Positive radial solutions to a `semilinear’ equation involving the Pucci’s operator

J. Differential Equations 199 (2004), no. 2, 376–393

2004
4

P. Felmer, A. Quaas

On critical exponents for the Pucci’s extremal operators

Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 5, 843–865

2003
3

P. Felmer, A. Quaas

Critical exponents for the Pucci’s extremal operators

C. R. Math. Acad. Sci. Paris 335 (2002), no. 11, 909–914

2002
2

J. Busca, A. Quaas

Qualitative properties for semilinear elliptic systems with non-Lipschitz nonlinearity

Nonlinear Anal. 50 (2002), no. 3, Ser. A: Theory Methods, 299–312

2002
1

P. Felmer, A. Quaas

On the strong maximum principle for quasilinear elliptic equations and systems

Adv. Differential Equations 7 (2002), no. 1, 25–46

2002

Proyectos Vigentes

Programa Nombre Proyecto Periodo
FONDECYT REGULAR 1190282 Results of semi-linear and fully nonlinear problems including nonlocal operators 2019 - 2022
FONDECYT REGULAR 1151180 Some Nonlinear Local and Non-Local Elliptic Equations 2015 - 2019